Records A293556 and their indices A293555 in A243822.
Michael Thomas De Vlieger, St. Louis, Missouri, 201710101400, updated 201711171130.

Contents:

1. Table 1: Records in A243822 and their indices.
2. Observations regarding Table 1.
3. Table 2: Appearance of terms of A244052 among records of A243822.
4. Observations regarding Table 2.

  +------------------------------------------------+
  | Table 1: Records in A243822 and their indices. |
  +------------------------------------------------+

n = index in this document.
A293555(n) = index of record r in A243822.
k = index of record A293556(n) in A244052.
s = A243822(n) = record in A243822.
tau(n) = A000005(n).
A293556(n) = A010846(n) = A243822(n) + A000005(n).
MN(n) = multiplicity notation = rev(A054841(n)), shorthand notation
    that lists exponents e of p, pi(p) conveyed by position from left.
    e.g., 60 = 2^2 * 3 * 5 = "211".

  n    A293555(n)  	  k      s(n) tau(n) A293556(n) MN(n)
--------------------------------------------------------------------
  1	            1	  1	      0	   1	      1	0                 
  2	            6	  4	      1	   4	      5	11                
  3	           10	  5	      2	   4	      6	101               
  4	           18	  7	      4	   6	     10	12                
  5	           30	  9	     10	   8	     18	111               
  6	           42	 10	     11	   8	     19	1101              
  7	           60	 11	     14	  12	     26	211               
  8	           78	   	     15	   8	     23	110001            
  9	           84	 12	     16	  12	     28	2101              
 10	           90	 13	     20	  12	     32	121               
 11	          126	   	     21	  12	     33	1201              
 12	          150	 15	     29	  12	     41	112               
 13	          210	 17	     52	  16	     68	1111              
 14	          330	 18	     61	  16	     77	11101             
 15	          390	 19	     64	  16	     80	111001            
 16	          420	 20	     72	  24	     96	2111              
 17	          630	 21	     91	  24	    115	1211              
 18	          840	 22	     99	  32	    131	3111              
 19	          990	   	    100	  24	    124	12101             
 20	         1050	 23	    121	  24	    145	1121              
 21	         1470	 25	    142	  24	    166	1112              
 22	         1890	 27	    151	  32	    183	1311              
 23	         2100	 28	    156	  36	    192	2121              
 24	         2310	 29	    251	  32	    283	11111             
 25	         2730	 30	    263	  32	    295	111101            
 26	         3570	 31	    281	  32	    313	1111001           
 27	         3990	 32	    290	  32	    322	11110001          
 28	         4620	 33	    334	  48	    382	21111             
 29	         5460	 34	    347	  48	    395	211101            
 30	         6930	 35	    404	  48	    452	12111             
 31	         8190	 36	    415	  48	    463	121101            
 32	         9240	 37	    441	  64	    505	31111             
 33	        10920	 38	    455	  64	    519	311101            
 34	        11550	 39	    503	  48	    551	11211             
 35	        13650	 40	    519	  48	    567	112101            
 36	        13860	 41	    521	  72	    593	22111             
 37	        16170	 42	    581	  48	    629	11121             
 38	        19110	   	    595	  48	    643	111201            
 39	        20790	 44	    627	  64	    691	13111             
 40	        23100	 45	    645	  72	    717	21211             
 41	        25410	 46	    695	  48	    743	11112             
 42	        30030	 48	   1097	  64	   1161	111111            
 43	        39270	 49	   1160	  64	   1224	1111101           
 44	        43890	 50	   1189	  64	   1253	11111001          
 45	        46410	 51	   1193	  64	   1257	1111011           
 46	        51870	 52	   1221	  64	   1285	11110101          
 47	        53130	 53	   1242	  64	   1306	111110001         
 48	        60060	 54	   1430	  96	   1526	211111            
 49	        78540	 55	   1501	  96	   1597	2111101           
 50	        87780	 56	   1535	  96	   1631	21111001          
 51	        90090	 57	   1683	  96	   1779	121111            
 52	       117810	 58	   1760	  96	   1856	1211101           
 53	       120120	 59	   1849	 128	   1977	311111            
 54	       150150	 60	   2048	  96	   2144	112111            
 55	       180180	 61	   2150	 144	   2294	221111            
 56	       210210	 62	   2324	  96	   2420	111211            
 57	       240240	 63	   2378	 160	   2538	411111            
 58	       270270	 64	   2517	 128	   2645	131111            
 59	       300300	 65	   2599	 144	   2743	212111            
 60	       330330	 66	   2740	  96	   2836	111121            
 61	       390390	 68	   2905	  96	   3001	111112            
 62	       420420	 69	   2936	 144	   3080	211211            
 63	       450450	 70	   3009	 144	   3153	122111            
 64	       480480	 71	   3031	 192	   3223	511111            
 65	       510510	 72	   4715	 128	   4843	1111111           
 66	       570570	 73	   4811	 128	   4939	11111101          
 67	       690690	 74	   4991	 128	   5119	111111001         
 68	       746130	 75	   5010	 128	   5138	11111011          
 69	       870870	 76	   5236	 128	   5364	1111110001        
 70	       930930	 77	   5308	 128	   5436	11111100001       
 71	      1021020	 78	   6033	 192	   6225	2111111           
 72	      1141140	 79	   6145	 192	   6337	21111101          
 73	      1381380	 80	   6354	 192	   6546	211111001         
 74	      1492260	 81	   6368	 192	   6560	21111011          
 75	      1531530	 82	   6986	 192	   7178	1211111           
 76	      1711710	 83	   7107	 192	   7299	12111101          
 77	      2042040	 84	   7672	 256	   7928	3111111           
 78	      2282280	 85	   7799	 256	   8055	31111101          
 79	      2552550	 86	   8361	 192	   8553	1121111           
 80	      2852850	 87	   8493	 192	   8685	11211101          
 81	      3063060	 88	   8811	 288	   9099	2211111           
 82	      3423420	 89	   8948	 288	   9236	22111101          
 83	      3573570	 90	   9388	 192	   9580	1112111           
 84	      3993990	 91	   9527	 192	   9719	11121101          
 85	      4084080	 92	   9690	 320	  10010	4111111           
 86	      4564560	 93	   9835	 320	  10155	41111101          
 87	      4594590	 94	  10158	 256	  10414	1311111           
 88	      5105100	 95	  10489	 288	  10777	2121111           
 89	      5615610	 96	  10928	 192	  11120	1111211           
 90	      6126120	 97	  11057	 384	  11441	3211111           
 91	      6276270	   	  11077	 192	  11269	11112101          
 92	      6636630	 98	  11548	 192	  11740	1111121           
 93	      7147140	 99	  11739	 288	  12027	2112111           
 94	      7657650	100	  12005	 288	  12293	1221111           
 95	      8168160	101	  12165	 384	  12549	5111111           
 96	      8678670	102	  12607	 192	  12799	1111112           
 97	      9189180	103	  12653	 384	  13037	2311111           
 98	      9699690	104	  19729	 256	  19985	11111111          
 99	     11741730	105	  20349	 256	  20605	111111101         
100	     13123110	106	  20673	 256	  20929	111111011         
101	     14804790	107	  21197	 256	  21453	1111111001        
102	     15825810	108	  21457	 256	  21713	11111110001       
103	     16546530	109	  21513	 256	  21769	1111110101        
104	     17687670	110	  21772	 256	  22028	11111101001       
105	     18888870	111	  22187	 256	  22443	111111100001      
106	     19399380	112	  24905	 384	  25289	21111111          
107	     23483460	113	  25621	 384	  26005	211111101         
108	     26246220	114	  25986	 384	  26370	211111011         
109	     29099070	115	  28540	 384	  28924	12111111          
110*	     35225190	116	  29317	 384	  29701	121111101         
111	     38798760	117	  31264	 512	  31776	31111111          
112	     46966920	118	  32082	 512	  32594	311111101         
113	     48498450	119	  33766	 384	  34150	11211111          
114	     58198140	120	  35628	 576	  36204	22111111          
115	     67897830	121	  37644	 384	  38028	11121111          
116	     77597520	122	  39020	 640	  39660	41111111          
117	     87297210	123	  40649	 512	  41161	13111111          
118	     96996900	124	  41967	 576	  42543	21211111          
119	    106696590	125	  43443	 384	  43827	11112111          
120	    116396280	126	  44261	 768	  45029	32111111          
121	    126095970	127	  45772	 384	  46156	11111211          
122	    135795660	128	  46657	 576	  47233	21121111          
123	    145495350	129	  47664	 576	  48240	12211111          
124	    155195040	130	  48434	 768	  49202	51111111          
125	    164894730	131	  49746	 384	  50130	11111121          
126	    174594420	132	  50246	 768	  51014	23111111          
127	    184294110	133	  51477	 384	  51861	11111112          
128	    193993800	134	  51912	 768	  52680	31211111          
129	    203693490	135	  52892	 576	  53468	12121111          
130	    213393180	136	  53650	 576	  54226	21112111          
131	    223092870	137	  82562	 512	  83074	111111111         
132	    281291010	138	  85542	 512	  86054	1111111101        
133	    300690390	139	  86466	 512	  86978	11111111001       
134	    340510170	140	  87656	 512	  88168	1111111011        
135	    358888530	141	  89086	 512	  89598	111111110001      
136	    397687290	142	  90702	 512	  91214	1111111100001     
137	    417086670	143	  91481	 512	  91993	11111111000001    
138	    446185740	144	 102979	 768	 103747	211111111         
139	    562582020	145	 106420	 768	 107188	2111111101        
140	    601380780	146	 107499	 768	 108267	21111111001       
141	    669278610	147	 117069	 768	 117837	121111111         
142	    843873030	148	 120804	 768	 121572	1211111101        
143	    892371480	149	 127820	1024	 128844	311111111         
144	   1115464350	150	 137221	 768	 137989	112111111         
145	   1338557220	151	 144738	1152	 145890	221111111         
146	   1561650090	152	 152108	 768	 152876	111211111         
147	   1784742960	153	 157880	1280	 159160	411111111         
148	   2007835830	154	 163870	1024	 164894	131111111         
149	   2230928700	155	 169035	1152	 170187	212111111         
150	   2454021570	156	 174326	 768	 175094	111121111         
151	   2677114440	157	 178156	1536	 179692	321111111         
152	   2900207310	158	 183232	 768	 184000	111112111         
153	   3123300180	159	 186933	1152	 188085	211211111         
154	   3346393050	160	 190797	1152	 191949	122111111         
155	   3569485920	161	 194091	1536	 195627	511111111         
156	   3792578790	162	 198382	 768	 199150	111111211         
157	   4015671660	163	 200978	1536	 202514	231111111         
158	   4238764530	164	 204977	 768	 205745	111111121         
159	   4461857400	165	 207323	1536	 208859	312111111         
160	   4684950270	166	 210701	1152	 211853	121211111         
161	   4908043140	167	 213587	1152	 214739	211121111         
162	   5131136010	168	 216766	 768	 217534	111111112         
163	   5354228880	169	 218318	1920	 220238	421111111         
164	   5577321750	170	 221836	1024	 222860	113111111         
165	   5800414620	171	 224258	1152	 225410	211112111         
166	   6023507490	172	 226599	1280	 227879	141111111         
167	   6246600360	173	 228757	1536	 230293	311211111         
168	   6469693230	174	 348646	1024	 349670	1111111111        
169	   6915878970	175	 351974	1024	 352998	11111111101       
170	   8254436190	176	 361444	1024	 362468	111111111001      
171	   8720021310	177	 362536	1024	 363560	11111111011       
172	   9146807670	178	 367324	1024	 368348	1111111110001     
173	   9592993410	179	 370150	1024	 371174	11111111100001    
174	  10407767370	180	 372013	1024	 373037	111111110101      
175	  10485364890	181	 375602	1024	 376626	111111111000001   
176	  11532931410	182	 377920	1024	 378944	1111111101001     
177	  11823922110	183	 383315	1024	 384339	1111111110000001  
178	  12929686770	184	 384112	1024	 385136	11111111001001    
179	  12939386460	185	 430088	1536	 431624	2111111111        
180	  13831757940	186	 433944	1536	 435480	21111111101       
181	  16508872380	187	 444924	1536	 446460	211111111001      
182	  17440042620	188	 446047	1536	 447583	21111111011       
183	  18293615340	189	 451768	1536	 453304	2111111110001     
184	  19185986820	190	 455060	1536	 456596	21111111100001    
185	  19409079690	191	 485640	1536	 487176	1211111111        
186	  20747636910	192	 489829	1536	 491365	12111111101       
187	  24763308570	193	 501771	1536	 503307	121111111001      
188	  25878772920	194	 528344	2048	 530392	3111111111        
189	  27663515880	195	 532773	2048	 534821	31111111101       
190	  32348466150	196	 564703	1536	 566239	1121111111        
191	  34579394850	197	 569341	1536	 570877	11211111101       
192	  38818159380	198	 594834	2304	 597138	2211111111        
193	  41495273820	199	 599624	2304	 601928	22111111101       
194	  45287852610	200	 622881	1536	 624417	1112111111        
195	  48411152790	201	 627819	1536	 629355	11121111101       
196	  51757545840	202	 646388	2560	 648948	4111111111        
197	  55327031760	203	 651449	2560	 654009	41111111101       
198	  58227239070	204	 669249	2048	 671297	1311111111        
199	  62242910730	205	 674438	2048	 676486	13111111101       
200	  64696932300	206	 689574	2304	 691878	2121111111        
201	  69158789700	207	 694854	2304	 697158	21211111101       
202	  71166625530	208	 709456	1536	 710992	1111211111        
203	  76074668670	209	 714816	1536	 716352	11112111101       
204	  77636318760	210	 725761	3072	 728833	3211111111        
205	  82990547640	211	 731216	3072	 734288	32111111101       
206	  84106011990	212	 744066	1536	 745602	1111121111        
207	  89906426610	213	 749595	1536	 751131	11111211101       
208	  90575705220	214	 759134	2304	 761438	2112111111        
209	  96822305580	215	 764745	2304	 767049	21121111101       
210	  97045398450	216	 774141	2304	 776445	1221111111        
211	 103515091680	217	 787662	3072	 790734	5111111111        
212	 109984784910	218	 802832	1536	 804368	1111112111        
213	 116454478140	219	 814340	3072	 817412	2311111111        
214	 122924171370	220	 828394	1536	 829930	1111111211        
215	 129393864600	221	 838880	3072	 841952	3121111111        
216	 135863557830	222	 851229	2304	 853533	1212111111        
217	 142333251060	223	 862429	2304	 864733	2111211111        
218	 148802944290	224	 874008	1536	 875544	1111111121        
219	 155272637520	225	 882155	3840	 885995	4211111111        
220	 161742330750	226	 894086	2048	 896134	1131111111        
221	 168212023980	227	 903666	2304	 905970	2111121111        
222	 174681717210	228	 912961	2560	 915521	1411111111        
223	 181151410440	229	 921760	3072	 924832	3112111111        
224	 187621103670	230	 932340	1536	 933876	1111111112        
225	 194090796900	231	 939244	3456	 942700	2221111111        
226	 200560490130	232	1454410	2048	1456458	11111111111       
227	 239378649510	233	1488865	2048	1490913	111111111101      
228	 255887521890	234	1500943	2048	1502991	111111111011      
229	 265257422430	235	1510476	2048	1512524	1111111111001     
230	 278196808890	236	1520871	2048	1522919	11111111110001    
231	 283551037770	237	1522564	2048	1524612	1111111110101     
232	 297382795710	238	1532974	2048	1535022	11111111101001    
233	 304075581810	239	1540983	2048	1543031	111111111100001   
234	 325046311590	240	1553131	2048	1555179	111111111010001   
235	 338431883790	241	1557242	2048	1559290	1111111110011     
236	 342893741190	242	1569498	2048	1571546	1111111111000001  
237	 366541585410	243	1581681	2048	1583729	1111111110100001  
238	 381711900570	244	1596245	2048	1598293	11111111110000001 
239	 394651287030	245	1604802	2048	1606850	111111111100000001
240	 401120980260	246	1778346	3072	1781418	21111111111       
241	 478757299020	247	1818099	3072	1821171	211111111101      
242	 511775043780	248	1831946	3072	1835018	211111111011      
243	 530514844860	249	1843101	3072	1846173	2111111111001     
244	 556393617780	250	1855149	3072	1858221	21111111110001    
245	 567102075540	251	1856969	3072	1860041	2111111110101     
246	 594765591420	252	1869030	3072	1872102	21111111101001    
247	 601681470390	253	1997575	3072	2000647	12111111111       
248	 718135948530	254	2040712	3072	2043784	121111111101      
249	 767662565670	255	2055677	3072	2058749	121111111011      
250	 795772267290	256	2067874	3072	2070946	1211111111001     
251	 802241960520	257	2166613	4096	2170709	31111111111       
252	 957514598040	258	2212232	4096	2216328	311111111101      
253	1002802450650	259	2308457	3072	2311529	11211111111       
254	1196893247550	260	2356095	3072	2359167	112111111101      
255	1203362940780	261	2428046	4608	2432654	22111111111       
256	1403923430910	262	2536449	3072	2539521	11121111111       
257	1604483921040	263	2630381	5120	2635501	41111111111       
258	1805044411170	264	2718799	4096	2722895	13111111111       
259	2005604901300	265	2798663	4608	2803271	21211111111       
260	2206165391430	266	2874776	3072	2877848	11112111111       
261	2406725881560	267	2941315	6144	2947459	32111111111       
262	2607286371690	268	3009782	3072	3012854	11111211111       
263	2807846861820	269	3069975	4608	3074583	21121111111       
264	3008407351950	270	3128462	4608	3133070	12211111111       
265	3208967842080	271	3182522	6144	3188666	51111111111       
266	3409528332210	272	3238675	3072	3241747	11111121111       
267	3610088822340	273	3286370	6144	3292514	23111111111       
268	3810649312470	274	3338111	3072	3341183	11111112111       
269	4011209802600	275	3381807	6144	3387951	31211111111       
270	4211770292730	276	3428382	4608	3432990	12121111111       
271	4412330782860	277	3471845	4608	3476453	21112111111       
272	4612891272990	278	3515369	3072	3518441	11111111211       
273	4813451763120	279	3551384	7680	3559064	42111111111       
274	5014012253250	280	3594359	4096	3598455	11311111111       
275	5214572743380	281	3632018	4608	3636626	21111211111       
276	5415133233510	282	3668614	5120	3673734	14111111111       
277	5615693723640	283	3703670	6144	3709814	31121111111       
278	5816254213770	284	3741846	3072	3744918	11111111121       
279	6016814703900	285	3772232	6912	3779144	22211111111       
280	6217375194030	286	3809412	3072	3812484	11111111112       
281	6417935684160	287	3837859	7168	3845027	61111111111       
282	6618496174290	288	3872222	4608	3876830	12112111111       
283	6819056664420	289	3903277	4608	3907885	21111121111       
284	7019617154550	290	3933674	4608	3938282	11221111111       
285	7220177644680	291	3959819	8192	3968011	33111111111       

////// Note //////

The sequence has been directly verified through term 110.
All terms 1 - 285 were generated using the tier-3 algorithm, which uses a necessary
but not sufficient condition that must be tested by A243822(m) = A010846(m) - A000005(m).

////// Observations //////

1. Visually, in aggregate, the column MN(n) resembles MN(A244052).
2. Terms in n appear in A244052 except {78, 126, 990, 19110, 6276270, ...}.
3. Primorials A002110 seem to divide this sequence into tiers as they
   do A244052.
4. The function MN(A244052(n)) has been studied deeply enough to furnish
   A288784 and A288813 regarding candidate numbers for inclusion in
   A244052 (i.e., a necessary-but-insufficient condition for A244052).
   MN of the terms in n but not in A244052 involve turbulent terms t
   that exceed 2kp_T#, often with depth 1, except in the case of 
   n = 78 which has depth 3. (See A244052). This seems to imply that
   a sequence similar to A288784 might be produced for this sequence
   that would serve a similar role that A288784 does for A244052.
   If this is true, then we might attain larger values of n without
   testing the full range of numbers up to a large limit.

  +-------------------------------------------------------------------+
  | Table 2: Appearance of terms of A244052 among records of A243822. |
  +-------------------------------------------------------------------+

k = index in this table.
m = A244052(k).
i = index of A293555.
s = A243822(m).
tau(m) = A000005(m).
r = A010846(m) = A243822(m) + A000005(m).
MN(n) = multiplicity notation = rev(A054841(n)), shorthand notation
    that lists exponents e of p, pi(p) conveyed by position from left.
    e.g., 60 = 2^2 * 3 * 5 = "211".

  k            	    m  	  i       s(m) tau(m)     r(m)   MN(m)
---------------------------------------------------------------------
  1	            1	  1	      0	   1	      1	0                 
  2	            2	   	      0	   2	      2	1                 
  3	            4	   	      0	   3	      3	2                 
  4	            6	  2	      1	   4	      5	11                
  5	           10	  3	      2	   4	      6	101               
  6	           12	   	      2	   6	      8	21                
  7	           18	  4	      4	   6	     10	12                
  8	           24	   	      3	   8	     11	31                
  9	           30	  5	     10	   8	     18	111               
 10	           42	  6	     11	   8	     19	1101              
 11	           60	  7	     14	  12	     26	211               
 12	           84	  9	     16	  12	     28	2101              
 13	           90	 10	     20	  12	     32	121               
 14	          120	   	     20	  16	     36	311               
 15	          150	 12	     29	  12	     41	112               
 16	          180	   	     26	  18	     44	221               
 17	          210	 13	     52	  16	     68	1111              
 18	          330	 14	     61	  16	     77	11101             
 19	          390	 15	     64	  16	     80	111001            
 20	          420	 16	     72	  24	     96	2111              
 21	          630	 17	     91	  24	    115	1211              
 22	          840	 18	     99	  32	    131	3111              
 23	         1050	 20	    121	  24	    145	1121              
 24	         1260	   	    120	  36	    156	2211              
 25	         1470	 21	    142	  24	    166	1112              
 26	         1680	   	    134	  40	    174	4111              
 27	         1890	 22	    151	  32	    183	1311              
 28	         2100	 23	    156	  36	    192	2121              
 29	         2310	 24	    251	  32	    283	11111             
 30	         2730	 25	    263	  32	    295	111101            
 31	         3570	 26	    281	  32	    313	1111001           
 32	         3990	 27	    290	  32	    322	11110001          
 33	         4620	 28	    334	  48	    382	21111             
 34	         5460	 29	    347	  48	    395	211101            
 35	         6930	 30	    404	  48	    452	12111             
 36	         8190	 31	    415	  48	    463	121101            
 37	         9240	 32	    441	  64	    505	31111             
 38	        10920	 33	    455	  64	    519	311101            
 39	        11550	 34	    503	  48	    551	11211             
 40	        13650	 35	    519	  48	    567	112101            
 41	        13860	 36	    521	  72	    593	22111             
 42	        16170	 37	    581	  48	    629	11121             
 43	        18480	   	    580	  80	    660	41111             
 44	        20790	 39	    627	  64	    691	13111             
 45	        23100	 40	    645	  72	    717	21211             
 46	        25410	 41	    695	  48	    743	11112             
 47	        27720	   	    670	  96	    766	32111             
 48	        30030	 42	   1097	  64	   1161	111111            
 49	        39270	 43	   1160	  64	   1224	1111101           
 50	        43890	 44	   1189	  64	   1253	11111001          
 51	        46410	 45	   1193	  64	   1257	1111011           
 52	        51870	 46	   1221	  64	   1285	11110101          
 53	        53130	 47	   1242	  64	   1306	111110001         
 54	        60060	 48	   1430	  96	   1526	211111            
 55	        78540	 49	   1501	  96	   1597	2111101           
 56	        87780	 50	   1535	  96	   1631	21111001          
 57	        90090	 51	   1683	  96	   1779	121111            
 58	       117810	 52	   1760	  96	   1856	1211101           
 59	       120120	 53	   1849	 128	   1977	311111            
 60	       150150	 54	   2048	  96	   2144	112111            
 61	       180180	 55	   2150	 144	   2294	221111            
 62	       210210	 56	   2324	  96	   2420	111211            
 63	       240240	 57	   2378	 160	   2538	411111            
 64	       270270	 58	   2517	 128	   2645	131111            
 65	       300300	 59	   2599	 144	   2743	212111            
 66	       330330	 60	   2740	  96	   2836	111121            
 67	       360360	   	   2729	 192	   2921	321111            
 68	       390390	 61	   2905	  96	   3001	111112            
 69	       420420	 62	   2936	 144	   3080	211211            
 70	       450450	 63	   3009	 144	   3153	122111            
 71	       480480	 64	   3031	 192	   3223	511111            
 72	       510510	 65	   4715	 128	   4843	1111111           
 73	       570570	 66	   4811	 128	   4939	11111101          
 74	       690690	 67	   4991	 128	   5119	111111001         
 75	       746130	 68	   5010	 128	   5138	11111011          
 76	       870870	 69	   5236	 128	   5364	1111110001        
 77	       930930	 70	   5308	 128	   5436	11111100001       
 78	      1021020	 71	   6033	 192	   6225	2111111           
 79	      1141140	 72	   6145	 192	   6337	21111101          
 80	      1381380	 73	   6354	 192	   6546	211111001         
 81	      1492260	 74	   6368	 192	   6560	21111011          
 82	      1531530	 75	   6986	 192	   7178	1211111           
 83	      1711710	 76	   7107	 192	   7299	12111101          
 84	      2042040	 77	   7672	 256	   7928	3111111           
 85	      2282280	 78	   7799	 256	   8055	31111101          
 86	      2552550	 79	   8361	 192	   8553	1121111           
 87	      2852850	 80	   8493	 192	   8685	11211101          
 88	      3063060	 81	   8811	 288	   9099	2211111           
 89	      3423420	 82	   8948	 288	   9236	22111101          
 90	      3573570	 83	   9388	 192	   9580	1112111           
 91	      3993990	 84	   9527	 192	   9719	11121101          
 92	      4084080	 85	   9690	 320	  10010	4111111           
 93	      4564560	 86	   9835	 320	  10155	41111101          
 94	      4594590	 87	  10158	 256	  10414	1311111           
 95	      5105100	 88	  10489	 288	  10777	2121111           
 96	      5615610	 89	  10928	 192	  11120	1111211           
 97	      6126120	 90	  11057	 384	  11441	3211111           
 98	      6636630	 92	  11548	 192	  11740	1111121           
 99	      7147140	 93	  11739	 288	  12027	2112111           
100	      7657650	 94	  12005	 288	  12293	1221111           
101	      8168160	 95	  12165	 384	  12549	5111111           
102	      8678670	 96	  12607	 192	  12799	1111112           
103	      9189180	 97	  12653	 384	  13037	2311111           
104	      9699690	 98	  19729	 256	  19985	11111111          
105	     11741730	 99	  20349	 256	  20605	111111101         
106	     13123110	100	  20673	 256	  20929	111111011         
107	     14804790	101	  21197	 256	  21453	1111111001        
108	     15825810	102	  21457	 256	  21713	11111110001       
109	     16546530	103	  21513	 256	  21769	1111110101        
110	     17687670	104	  21772	 256	  22028	11111101001       
111	     18888870	105	  22187	 256	  22443	111111100001      
112	     19399380	106	  24905	 384	  25289	21111111          
113	     23483460	107	  25621	 384	  26005	211111101         
114	     26246220	108	  25986	 384	  26370	211111011         
115	     29099070	109	  28540	 384	  28924	12111111          
116*	     35225190	110	  29317	 384	  29701	121111101         
117	     38798760	111	  31264	 512	  31776	31111111          
118	     46966920	112	  32082	 512	  32594	311111101         
119	     48498450	113	  33766	 384	  34150	11211111          
120	     58198140	114	  35628	 576	  36204	22111111          
121	     67897830	115	  37644	 384	  38028	11121111          
122	     77597520	116	  39020	 640	  39660	41111111          
123	     87297210	117	  40649	 512	  41161	13111111          
124	     96996900	118	  41967	 576	  42543	21211111          
125	    106696590	119	  43443	 384	  43827	11112111          
126	    116396280	120	  44261	 768	  45029	32111111          
127	    126095970	121	  45772	 384	  46156	11111211          
128	    135795660	122	  46657	 576	  47233	21121111          
129	    145495350	123	  47664	 576	  48240	12211111          
130	    155195040	124	  48434	 768	  49202	51111111          
131	    164894730	125	  49746	 384	  50130	11111121          
132	    174594420	126	  50246	 768	  51014	23111111          
133	    184294110	127	  51477	 384	  51861	11111112          
134	    193993800	128	  51912	 768	  52680	31211111          
135	    203693490	129	  52892	 576	  53468	12121111          
136	    213393180	130	  53650	 576	  54226	21112111          
137	    223092870	131	  82562	 512	  83074	111111111         
138	    281291010	132	  85542	 512	  86054	1111111101        
139	    300690390	133	  86466	 512	  86978	11111111001       
140	    340510170	134	  87656	 512	  88168	1111111011        
141	    358888530	135	  89086	 512	  89598	111111110001      
142	    397687290	136	  90702	 512	  91214	1111111100001     
143	    417086670	137	  91481	 512	  91993	11111111000001    
144	    446185740	138	 102979	 768	 103747	211111111         
145	    562582020	139	 106420	 768	 107188	2111111101        
146	    601380780	140	 107499	 768	 108267	21111111001       
147	    669278610	141	 117069	 768	 117837	121111111         
148	    843873030	142	 120804	 768	 121572	1211111101        
149	    892371480	143	 127820	1024	 128844	311111111         
150	   1115464350	144	 137221	 768	 137989	112111111         
151	   1338557220	145	 144738	1152	 145890	221111111         
152	   1561650090	146	 152108	 768	 152876	111211111         
153	   1784742960	147	 157880	1280	 159160	411111111         
154	   2007835830	148	 163870	1024	 164894	131111111         
155	   2230928700	149	 169035	1152	 170187	212111111         
156	   2454021570	150	 174326	 768	 175094	111121111         
157	   2677114440	151	 178156	1536	 179692	321111111         
158	   2900207310	152	 183232	 768	 184000	111112111         
159	   3123300180	153	 186933	1152	 188085	211211111         
160	   3346393050	154	 190797	1152	 191949	122111111         
161	   3569485920	155	 194091	1536	 195627	511111111         
162	   3792578790	156	 198382	 768	 199150	111111211         
163	   4015671660	157	 200978	1536	 202514	231111111         
164	   4238764530	158	 204977	 768	 205745	111111121         
165	   4461857400	159	 207323	1536	 208859	312111111         
166	   4684950270	160	 210701	1152	 211853	121211111         
167	   4908043140	161	 213587	1152	 214739	211121111         
168	   5131136010	162	 216766	 768	 217534	111111112         
169	   5354228880	163	 218318	1920	 220238	421111111         
170	   5577321750	164	 221836	1024	 222860	113111111         
171	   5800414620	165	 224258	1152	 225410	211112111         
172	   6023507490	166	 226599	1280	 227879	141111111         
173	   6246600360	167	 228757	1536	 230293	311211111         
174	   6469693230	168	 348646	1024	 349670	1111111111        
175	   6915878970	169	 351974	1024	 352998	11111111101       
176	   8254436190	170	 361444	1024	 362468	111111111001      
177	   8720021310	171	 362536	1024	 363560	11111111011       
178	   9146807670	172	 367324	1024	 368348	1111111110001     
179	   9592993410	173	 370150	1024	 371174	11111111100001    
180	  10407767370	174	 372013	1024	 373037	111111110101      
181	  10485364890	175	 375602	1024	 376626	111111111000001   
182	  11532931410	176	 377920	1024	 378944	1111111101001     
183	  11823922110	177	 383315	1024	 384339	1111111110000001  
184	  12929686770	178	 384112	1024	 385136	11111111001001    
185	  12939386460	179	 430088	1536	 431624	2111111111        
186	  13831757940	180	 433944	1536	 435480	21111111101       
187	  16508872380	181	 444924	1536	 446460	211111111001      
188	  17440042620	182	 446047	1536	 447583	21111111011       
189	  18293615340	183	 451768	1536	 453304	2111111110001     
190	  19185986820	184	 455060	1536	 456596	21111111100001    
191	  19409079690	185	 485640	1536	 487176	1211111111        
192	  20747636910	186	 489829	1536	 491365	12111111101       
193	  24763308570	187	 501771	1536	 503307	121111111001      
194	  25878772920	188	 528344	2048	 530392	3111111111        
195	  27663515880	189	 532773	2048	 534821	31111111101       
196	  32348466150	190	 564703	1536	 566239	1121111111        
197	  34579394850	191	 569341	1536	 570877	11211111101       
198	  38818159380	192	 594834	2304	 597138	2211111111        
199	  41495273820	193	 599624	2304	 601928	22111111101       
200	  45287852610	194	 622881	1536	 624417	1112111111        
201	  48411152790	195	 627819	1536	 629355	11121111101       
202	  51757545840	196	 646388	2560	 648948	4111111111        
203	  55327031760	197	 651449	2560	 654009	41111111101       
204	  58227239070	198	 669249	2048	 671297	1311111111        
205	  62242910730	199	 674438	2048	 676486	13111111101       
206	  64696932300	200	 689574	2304	 691878	2121111111        
207	  69158789700	201	 694854	2304	 697158	21211111101       
208	  71166625530	202	 709456	1536	 710992	1111211111        
209	  76074668670	203	 714816	1536	 716352	11112111101       
210	  77636318760	204	 725761	3072	 728833	3211111111        
211	  82990547640	205	 731216	3072	 734288	32111111101       
212	  84106011990	206	 744066	1536	 745602	1111121111        
213	  89906426610	207	 749595	1536	 751131	11111211101       
214	  90575705220	208	 759134	2304	 761438	2112111111        
215	  96822305580	209	 764745	2304	 767049	21121111101       
216	  97045398450	210	 774141	2304	 776445	1221111111        
217	 103515091680	211	 787662	3072	 790734	5111111111        
218	 109984784910	212	 802832	1536	 804368	1111112111        
219	 116454478140	213	 814340	3072	 817412	2311111111        
220	 122924171370	214	 828394	1536	 829930	1111111211        
221	 129393864600	215	 838880	3072	 841952	3121111111        
222	 135863557830	216	 851229	2304	 853533	1212111111        
223	 142333251060	217	 862429	2304	 864733	2111211111        
224	 148802944290	218	 874008	1536	 875544	1111111121        
225	 155272637520	219	 882155	3840	 885995	4211111111        
226	 161742330750	220	 894086	2048	 896134	1131111111        
227	 168212023980	221	 903666	2304	 905970	2111121111        
228	 174681717210	222	 912961	2560	 915521	1411111111        
229	 181151410440	223	 921760	3072	 924832	3112111111        
230	 187621103670	224	 932340	1536	 933876	1111111112        
231	 194090796900	225	 939244	3456	 942700	2221111111        
232	 200560490130	226	1454410	2048	1456458	11111111111       
233	 239378649510	227	1488865	2048	1490913	111111111101      
234	 255887521890	228	1500943	2048	1502991	111111111011      
235	 265257422430	229	1510476	2048	1512524	1111111111001     
236	 278196808890	230	1520871	2048	1522919	11111111110001    
237	 283551037770	231	1522564	2048	1524612	1111111110101     
238	 297382795710	232	1532974	2048	1535022	11111111101001    
239	 304075581810	233	1540983	2048	1543031	111111111100001   
240	 325046311590	234	1553131	2048	1555179	111111111010001   
241	 338431883790	235	1557242	2048	1559290	1111111110011     
242	 342893741190	236	1569498	2048	1571546	1111111111000001  
243	 366541585410	237	1581681	2048	1583729	1111111110100001  
244	 381711900570	238	1596245	2048	1598293	11111111110000001 
245	 394651287030	239	1604802	2048	1606850	111111111100000001
246	 401120980260	240	1778346	3072	1781418	21111111111       
247	 478757299020	241	1818099	3072	1821171	211111111101      
248	 511775043780	242	1831946	3072	1835018	211111111011      
249	 530514844860	243	1843101	3072	1846173	2111111111001     
250	 556393617780	244	1855149	3072	1858221	21111111110001    
251	 567102075540	245	1856969	3072	1860041	2111111110101     
252	 594765591420	246	1869030	3072	1872102	21111111101001    
253	 601681470390	247	1997575	3072	2000647	12111111111       
254	 718135948530	248	2040712	3072	2043784	121111111101      
255	 767662565670	249	2055677	3072	2058749	121111111011      
256	 795772267290	250	2067874	3072	2070946	1211111111001     
257	 802241960520	251	2166613	4096	2170709	31111111111       
258	 957514598040	252	2212232	4096	2216328	311111111101      
259	1002802450650	253	2308457	3072	2311529	11211111111       
260	1196893247550	254	2356095	3072	2359167	112111111101      
261	1203362940780	255	2428046	4608	2432654	22111111111       
262	1403923430910	256	2536449	3072	2539521	11121111111       
263	1604483921040	257	2630381	5120	2635501	41111111111       
264	1805044411170	258	2718799	4096	2722895	13111111111       
265	2005604901300	259	2798663	4608	2803271	21211111111       
266	2206165391430	260	2874776	3072	2877848	11112111111       
267	2406725881560	261	2941315	6144	2947459	32111111111       
268	2607286371690	262	3009782	3072	3012854	11111211111       
269	2807846861820	263	3069975	4608	3074583	21121111111       
270	3008407351950	264	3128462	4608	3133070	12211111111       
271	3208967842080	265	3182522	6144	3188666	51111111111       
272	3409528332210	266	3238675	3072	3241747	11111121111       
273	3610088822340	267	3286370	6144	3292514	23111111111       
274	3810649312470	268	3338111	3072	3341183	11111112111       
275	4011209802600	269	3381807	6144	3387951	31211111111       
276	4211770292730	270	3428382	4608	3432990	12121111111       
277	4412330782860	271	3471845	4608	3476453	21112111111       
278	4612891272990	272	3515369	3072	3518441	11111111211       
279	4813451763120	273	3551384	7680	3559064	42111111111       
280	5014012253250	274	3594359	4096	3598455	11311111111       
281	5214572743380	275	3632018	4608	3636626	21111211111       
282	5415133233510	276	3668614	5120	3673734	14111111111       
283	5615693723640	277	3703670	6144	3709814	31121111111       
284	5816254213770	278	3741846	3072	3744918	11111111121       
285	6016814703900	279	3772232	6912	3779144	22211111111       
286	6217375194030	280	3809412	3072	3812484	11111111112       
287	6417935684160	281	3837859	7168	3845027	61111111111       
288	6618496174290	282	3872222	4608	3876830	12112111111       
289	6819056664420	283	3903277	4608	3907885	21111121111       
290	7019617154550	284	3933674	4608	3938282	11221111111       
291	7220177644680	285	3959819	8192	3968011	33111111111       

////// Note //////

The sequence has been directly verified through term 116.
All terms 1 - 291 were generated using the tier-3 algorithm, which uses a necessary
but not sufficient condition that must be tested by A243822(m) = A010846(m) - A000005(m).

////// Observations //////

1. Terms m in A244052 appear in n except 
   {2, 4, 12, 24, 120, 180, 1260, 1680, 18480, 27720, 360360, ...}.
2. Terms m in A244052 not in n seem to have tau(m) 
   significantly greater than surrounding values.

////// Revision Record //////

201710101400 created, range 1 <= n <= 10^6.
201710110700 range increased to 1 <= n <= 3 * 10^6.
201710111500 range increased to 1 <= n <= 5 * 10^6.
201710111915 A293555 and A293556 reserved.
201710120545 range increased to 1 <= n <= 7 * 10^6.
201710121200 range increased to 1 <= n <= 8 * 10^6.
201710130230 range increased to 1 <= n <= 9 * 10^6.
201710140130 range increased to 1 <= n <= 10^7.
201710151930 range increased to 1 <= n <= 15 * 10^6.
201710160730 range increased to 1 <= n <= 17 * 10^6.
201710161545 range increased to 1 <= n <= 18 * 10^6.
201710171015 range increased to 1 <= n <= 21 * 10^6.
-----
201710172100 tier-3 algorithm used up to A002110(10) - 1.
201710180800 tier-3 algorithm used up to A002110(12) - 1.
201710241130 verified to 26 * 10^6.
201710261300 verified to 29 * 10^6.
201710271845 verified to 32 * 10^6.
201711070330 verified to 36 * 10^6.
201711171130 finalize revisions.

(eof)